Rewrite as a simplified fraction. ${2.17\overline{8} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 2178.8888...\\ 100x &= 217.8888...\end{align*}}$ Subtracting the two equations, we have: ${900x = 1961}$ ${x = \dfrac{1961}{900}} \text{or} {2 \dfrac{161}{900}}$